Theoretical cellular automata have been proposed as models for many physical phenomena from music to quantum mechanics. My question concerns the reverse:
Is there a simple physical system that emulates a theoretical cellular automaton?
A computer running CA software such as Hashlife can be considered an (extremely complex) physical system that behaves according to the rules of the programmed CA. I am however looking for something much simpler, such as a set of dominoes that topple each other in a fashion conforming to the rules of a certain CA, wave interference patterns that model a CA etc.
The point is that there have been enormous advances in CA theory lately (such as the discovery of the first self-replicating pattern in Conway's Game of Life in November 2013) that it would be interesting if these patterns could simply be "set up" in the physical world somehow and then they would evolve according to the CA rules without requiring a computer to simulate the rules. In the long run, this might even lead to the creation self-replicating physical systems.